How can I apply an auto-correlation to a Radon Transformation?

I have the following code

I = imread('img.jpg');
I = rgb2gray(I);
theta = 1:180;
[R,xp] = radon(I,theta);

how can I apply auto-correlation on this radon transformation on an image?

I have the following formula for auto-correlation which I want to apply:

where g(s,0) is the radon transformation. How can I implement this in Matlab? or is there an equivalent function that I can use?

Thank you in advance!

Answer 1

[Matt J]

Just apply conv() or xcorr(), if you have it, to each of the columns of R. A simple for-loop will do.

[Andrei]

Thanks for the reply!

Answer 2

[Matt J]

You can also use Fourier methods, something like

c=ifft( fft(R).*conj(fft(R)) )
c=bsxfun(@rdivide,c,sum(R.^2,1));

[Andrei]

should there be a difference between this method and the one above? I'm getting different results.

[Bjorn Gustavsson]

Just shooting from the hip on this one. In principal the results should be the same, within numerical accuracies- but if you use xcorr it might give you some default weigthing of the different lags.

[Matt J]

The correlation/convolution, when implemented using ffts, is circulant. You will have to zero pad to make it equivalent to linear convolution.